Deterministic production of N-photon states from a single atom-cavity system

We propose a mechanism for producing N-photon states on demand leaking from a single-mode optical cavity interacting with a single atom and a laser pulse. The number of photons can be chosen because it is determined by the Zeeman substructure of the ground state of the atom and its initial state. The deterministic generation of traveling light of 1 <= n <= 2F photons is achieved, when a circularly polarized laser pulse completely transfers the atomic population between Zeeman sublevels of the ground hyperfine state F through far-detuned Raman scattering, thus producing linearly polarized cavity photons. We describe analytically the evolution of optical field taking into account the spontaneous losses and the cavity damping. We analyze the photon statistics showing that it is close to Poissonian light. We show also that this technique provides a deterministic source of a train of identical multiphoton states with a definite number of photons if a sequence of left-and right-circularly polarized laser pulses is applied. The scheme expands the possibilities for using complex internal states of light to transmit data.